Construction of m-cube mesh networks using Petri nets

Petri nets have been used extensively in behavior modeling of finite state machines for a very long time since it is more expressible and gives parallelism in the designing of models. The problem of analysis in concurrent systems has been a field of interest for many researchers. Still, only reachability and its systematic enumeration were proven to be useful because of simplified concepts and easy applicability. This article shows the reachability in concurrent nets and topological properties reflected in its reachability analysis. It also discusses how a reachability tree is reduced to a graph by homomorphism and how we can find multi-dimensional topological networks with a class of Petri nets.